#!/usr/bin/env python
from socket import create_connection
from sys import *
from fractions import gcd
from numpy import random
from operator import *
from time import *

def extended_euclidean(a, b):	
	x = 0
	lastx = 1
	y = 1
	lasty = 0
	
	while b != 0:
		q = a // b
		a, b = b, a % b		
		x, lastx = (lastx - q * x, x)
		y, lasty = (lasty - q * y, y)
	return (a, lastx, lasty)
	
def inverse(var, module):
	v = extended_euclidean(var,module)
	return (v[0]==1)*(v[1] % module)

def CRT(RemList,ModulList):
	N  = reduce(mul,ModulList)        		# multiply ModulList together
	Ns = [N/mi for mi in ModulList]   		# create list of all N/multiply
	ys = [inverse(Ni, mi) for Ni,mi in zip(Ns,ModulList)] # get inverse elements of Ni by module mi
	return (reduce(add,[ri*Ni*yi for ri,Ni,yi in zip(RemList,Ns,ys)]) % N,N)

g = 2
primes = [37975227936943673922808872755445627854565536638199, 40094690950920881030683735292761468389214899724061,
6122421090493547576937037317561418841225758554253106999, 5846418214406154678836553182979162384198610505601062333,
327414555693498015751146303749141488063642403240171463406883, 693342667110830181197325401899700641361965863127336680673013]

reminders = []

print "Receiving reminders..."
for i in xrange(0,6,1):
	conn = create_connection(('109.233.61.11', 3120));

	data = conn.recv(1024);
	conn.send(str(primes[i]) + "\n")
	sleep(0.1)

	data = conn.recv(1024);
	conn.send(str(g) + "\n")
	sleep(0.1)

	data = conn.recv(1024);
	res1 = data.split()[-1]

	conn = create_connection(('109.233.61.11', 3120));

	data = conn.recv(1024);
	conn.send(str(primes[i]) + "\n")
	sleep(0.1)

	data = conn.recv(1024);
	conn.send(str(primes[i]-g) + "\n")
	sleep(0.1)

	data = conn.recv(1024);
	res2 = data.split()[-1]

	reminders.append((int(res1)+int(res2))%primes[i])

print "Using Chinese Remainder Theorem to recover flag..."

result =  CRT(reminders,primes)
f = result[0]/2
encoded_flag = str(hex(f))[2:-1]
flag = encoded_flag.decode("hex")
print flag